What are some a Pharaoh's duties?

Well, the Pharaohs mostly had privileges and powers: they were believed to be Gods so they could command other people to follow their will.

Noone could enforce this, but Pharaohs were expected to lead Egypt: they would make major decisions, settle conflicts, and generally ensure peace and unity in Egypt (there was actually a word for this: Ma'at). 

Their other duties were mostly religious duties, ceremonies and building temples.